Agoogolplex is thelarge number10googol, or equivalently,1010100 or1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Written out in ordinarydecimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by agoogol of zeroes. Its prime factorization is 2googol ×5googol.
In 1920,Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the termgoogol, which is 10100, and then proposed the further termgoogolplex to be "one, followed by writing zeroes until you get tired".[1] Kasner decided to adopt a more formal definition because "different people get tired at different times and it would never do to haveCarnera [be] a better mathematician thanDr. Einstein, simply because he had more endurance and could write for longer".[2] It thus became standardized to 10(10100) = 1010100, due to theright-associativity ofexponentiation.[3]
A typical book can be printed with 106 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 1094 such books to print all the zeros of a googolplex (that is, printing a googol zeros).[4]If each book had a mass of 100 grams, all of them would have a total mass of 1093 kilograms. In comparison,Earth's mass is 5.97 × 1024 kilograms,[5] the mass of theMilky Way galaxy is estimated at 1.8 × 1042 kilograms,[6] and the total mass of all the stars in theobservable universe is estimated at 2 × 1052 kg.[7]
To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly 5 × 1040.
Inpure mathematics, there are several notational methods for representinglarge numbers by which themagnitude of a googolplex could be represented, such astetration,hyperoperation,Knuth's up-arrow notation,Steinhaus–Moser notation, orConway chained arrow notation.
In thePBS science programCosmos: A Personal Voyage,Episode 9: "The Lives of the Stars",astronomer and television personalityCarl Sagan estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of theobservable universe is filled with finedust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of differentcombinations in which the particles could be arranged and numbered would be about one googolplex.[8][9]
1097 is a high estimate of the elementary particles existing in the visible universe (not includingdark matter), mostly photons and other massless force carriers.[10]
Theresidues (modn) of a googolplex, starting with mod 1, are:
This sequence is the same as the sequence ofresidues (modn) of a googol up until the 17th position.
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The dictionary definition ofgoogolplex at Wiktionary